Enigma 1665: Football league
3 December 2011
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From New Scientist #2831, 24th September 2011 [link]
My local football league has five teams, which each play each of the other teams twice. Three points are given for a win, and 1 point for a draw. At the end of the season, all five teams tied with the same number of points, so they were ordered by goal difference, which gave a clear winner. The team that drew the most games also won a game against the team that came top of the league.
How many games did the team that came top of the league win, draw and lose?